01 - Preheat the oven to 350°F. Grease and line a 9-inch round cake pan with parchment paper.
02 - In a small saucepan, melt 1 cup unsalted butter over medium heat. Cook, stirring, until foamy with brown flecks and a nutty aroma forms. Remove from heat and let cool slightly.
03 - In a medium bowl, whisk together the all-purpose flour, baking soda, baking powder, and salt.
04 - In a large bowl, mix the cooled brown butter with granulated sugar and light brown sugar. Beat in the eggs, one at a time. Stir in the mashed bananas and vanilla extract.
05 - Fold the dry mixture into the wet ingredients. Gently add the sour cream and mix until just combined; do not over-mix.
06 - Transfer the batter into the prepared cake pan. Smooth the surface and bake for 40 to 45 minutes, or until a toothpick inserted in the center emerges clean. Cool completely on a wire rack.
07 - In a dry saucepan, heat granulated sugar over medium heat, stirring constantly, until melted and amber in color. Whisk in the unsalted butter until melted. Slowly add heavy cream (the mixture will bubble), then stir in flaky sea salt. Allow to reach room temperature.
08 - In a bowl, beat softened unsalted butter until creamy. Gradually blend in powdered sugar and cooled salted caramel sauce. Add milk as needed to reach desired consistency.
09 - Once the cake is fully cool, apply the caramel frosting or generously drizzle salted caramel sauce over the top. Add extra sea salt flakes for garnish if desired.